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To prove that

\(\displaystyle sin^{-1}(ix)=2n\pi\pm i log(\sqrt{1+x^2}+x)\)

I can prove \(\displaystyle sin^{-1}(ix)=2n\pi+ i log(\sqrt{1+x^2}+x)\)

but facing problem to prove

\(\displaystyle sin^{-1}(ix)=2n\pi- i log(\sqrt{1+x^2}+x)\)

Help please

\(\displaystyle sin^{-1}(ix)=2n\pi\pm i log(\sqrt{1+x^2}+x)\)

I can prove \(\displaystyle sin^{-1}(ix)=2n\pi+ i log(\sqrt{1+x^2}+x)\)

but facing problem to prove

\(\displaystyle sin^{-1}(ix)=2n\pi- i log(\sqrt{1+x^2}+x)\)

Help please

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